Subtraction · Technique guide
Mental Subtraction Tricks
By Robert Hansson, Kung Fu Math
Borrowing is the reason many people dislike subtraction. Crossing out digits works on paper, but in your head it means remembering which column lent what. The good news is that mental subtraction rarely needs borrowing at all.
Subtraction measures a distance between two numbers. Once you think of it that way, you can travel that distance in whatever steps feel easiest: jump up from the smaller number, move both numbers together, or round and correct.
01
Count up
Instead of taking away, start at the smaller number and count up to the larger one in friendly jumps. Add the jumps together. This is how shopkeepers used to give change, and it removes borrowing completely.
Worked example
1 003 − 768
- → 768 → 800 is 32
- → 800 → 1 000 is 200
- → 1 000 → 1 003 is 3
- → 32 + 200 + 3 = 235
Answer: 235
Practice: Try 500 − 278, 2 012 − 1 856 and 91 − 47.
02
Round and compensate
If you subtract a number close to a round one, subtract the round number and give back the difference. Subtracting 199 is subtracting 200 and adding 1 back.
Worked example
843 − 297
- → 297 is 300 − 3
- → 843 − 300 = 543
- → You took 3 too many, so 543 + 3 = 546
Answer: 546
Practice: Try 625 − 198, 1 450 − 999 and 82 − 39.
03
Shift both numbers
The distance between two numbers does not change if you move both by the same amount. Add or subtract something from both so that the number being subtracted becomes round.
Worked example
72 − 38
- → Add 2 to both: 74 − 40
- → 74 − 40 = 34
Answer: 34
Practice: Try 83 − 47, 514 − 296 and 7.3 − 2.8.
04
Subtract from 1 000
To subtract any number from a power of ten, take every digit from 9 and the last digit from 10. This is a classic trick for working out change and complements.
Worked example
1 000 − 374
- → 3 from 9 is 6
- → 7 from 9 is 2
- → 4 from 10 is 6
Answer: 626
Practice: Try 1 000 − 528, 10 000 − 3 742 and 100 − 63.
05
Left to right
When no borrowing is needed, subtract place by place from the left. If a column would need borrowing, combine it with the column before: 74 − 38 is easier as 74 − 30 − 8.
Worked example
865 − 432
- → 865 − 400 = 465
- → 465 − 30 = 435
- → 435 − 2 = 433
Answer: 433
Practice: Try 978 − 543, 6 548 − 2 315 and 74 − 38.
Common mistakes
- Compensating the wrong way. Subtracting too much means you must add back.
- Shifting the numbers in opposite directions. Both must move the same amount and in the same direction.
- Forgetting a jump when counting up. Write the jumps on your fingers if needed.
Summary
- Think of subtraction as the distance between two numbers.
- Count up in friendly jumps or shift both numbers to make one round.
- Use the 9s and 10 rule to subtract from 100, 1 000 or 10 000.
Into the dojo
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